The study of statistical inference in GANs was initiated in the
recent important paper of [1]}.
These authors were the first to consider the consistency and asymptotic
normality of the sample GAN solutions \(\hat{\gamma }_{n}\)  and \(\hat{\delta }_{n}\) 
as estimators of the population GAN solutions \(\gamma _{0}\)  and \(\delta _{0}\) .
A key assumption these authors make is that the population GAN problem
(REF ) has a single, unique solution \((\gamma _{0},\delta _{0})\) .
However, as [1]} acknowledge,
this assumption is unrealistic in practical GAN applications.
On the contrary,
as the objective function \(f(\gamma ,\delta )\)  in (REF )
is parameterized using complicated neural networks \(G\)  and \(D\) ,
it is essentially guaranteed to have an extremely large number of
solutions (for related discussion, see [3]}).
One reason for this prevalence of multiple solutions is the inherent
non-identifiability of heavily parameterized neural networks.
